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Probability

Fill In the Blanks

131. The probability of an event that cannot happen is ________ Such an event is called __________.

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132. The probability of an event that is certain to happen is ________ Such an event is called _________.

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133. The sum of the probabilities of all the elemen-tary events of an experiment is ______.

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Short Answer Type

134. Which of the following arguments are correct and which are not correct ? Give reasons for your answer.

135. Two customers Shyam and Ekta are visiting a particular shop in the same weak (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on (i) the same day? (ii) consecutive days? (iii) different days?

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136. A die is a numbered in such a way that its face show the numbers 1, 2, 2, 3, 3, 6. It is thrown two times and the total score in two throws is noted. Complete the following table which gives a few values of the total score on the two throws :

What is the probability that the total scene is (i) even, (ii) 6, (iii) at least 6.

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137. A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of red ball, find the number of blue balls in the bag.

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138.
A box contains 12 balls out of which x are black. If one ball is drawn at random from the box, what is the probability that it will be a black ball? If 6 more black balls are put in the box, the probability of drawing a black ball is now double of what it was before. Find x.

Number of black balls in the box = x
Total number of balls in the box = 12

i.e., n(S) = 12

(0 Let A be the favourable outcomes of getting black ball, then
n(A) = x
Therefore,

P(A) = $fraction numerator n left parenthesis A right parenthesis over denominator n left parenthesis S right parenthesis end fraction equals x over 12$

(ii) Number of white balls in the box = x + 6 Total number of balls in the box = 12 + 6 = 18. i.e., n(S) = 18
Let B be the favourable outcomes of getting new white balls, then
n(B) = x + 6
Therefore,

P(B) = $fraction numerator straight n left parenthesis straight B right parenthesis over denominator straight n left parenthesis straight S right parenthesis end fraction equals fraction numerator x plus 6 over denominator 18 end fraction$
Now according to question

P(B) = 2P(A)

$rightwards double arrow space space space space space space space space space space space space fraction numerator straight x plus 6 over denominator 18 end fraction equals 2 open parentheses x over 12 close parentheses rightwards double arrow space space space space space space space space space space space space fraction numerator x plus 6 over denominator 18 end fraction equals fraction numerator 2 x over denominator 12 end fraction rightwards double arrow space space space space space space space space space space space space space fraction numerator x plus 6 over denominator 18 end fraction equals fraction numerator 2 x over denominator 12 end fraction rightwards double arrow space space space space space space space space space space space space space fraction numerator x plus 6 over denominator 3 end fraction equals x over 6 rightwards double arrow space space space space space space space space space space space space space space fraction numerator x plus 6 over denominator 3 end fraction equals x space rightwards double arrow space space space space space space space space space space space space space 3 x space equals space x plus 6 rightwards double arrow space space space space space space space space space space space space space space 2 x space equals space 6 rightwards double arrow space space space space space space space space space space space space space space space x space equals space 3 space space space space space space space space space$

Hence, the number of white balls = 3.

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139. A jar contains 24 marbles, some are green and others are blue. If a marble is drawn at random from the jar, the probability that it is green is

2 over 3

Find the number of blue balls in the jar.

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140. A box contains cards marked with numbers 5 to 20. A card is drawn from the bag at random. Find the probability of getting a number which is a perfect square.

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